This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice.

The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp–Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp–Leone (TPITL) distribution. The power inverted Topp–Leone and the inverted Topp–Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp–Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.

This work uses the inverse-power transformation to create the inverse power Ramos–Louzada distribution (IPRLD), a novel two-parameter version of the Ramos–Louzada distribution. The failure rate of the new distribution can be represented by a reverse bathtub shape, a rising shape, or a decreasing shape, making it appropriate for a range of real data. Asymmetrical and unimodal densities can be produced via the IPRLD. Its mathematical characteristics are computed in some cases. The novel proposed model’s structural characteristics are derived. To estimate the model parameters, several estimating strategies are explored, including ten classical methods. Simulation results with their partial and total ranks are used to evaluate the ranking and behavior of various approaches. Finally, two real-world datasets are used to experimentally show the suggested distribution’s adaptability. The analysis of the data reveals that the introduced distribution offers a better fit than some significant rival distributions, including the inverse Ramos–Louzada, inverse power Burr Hatke, inverse Nakagami-M, inverse log-logistic, inverse weighted Lindley, inverse Lindley, and Ramos–Louzada.

A new two-parameter power Zeghdoudi distribution (PZD) is suggested as a modification of the Zeghdoudi distribution using the power transformation method. As a result, the PZD may have increasing, decreasing, and unimodal probability density function and decreasing mean residual life function. In addition, other properties are presented, such as moments, order statistics, reliability measures, Bonferroni and Lorenz curves, Gini index, stochastic ordering, mean and median deviations, and quantile function. Following this, a section is devoted to the related model parameters which are estimated using the maximum likelihood estimation method, the weighted least squares and least squares methods, the maximum product of spacing method, the Cramer–von Mises method, and the right-tail and left-tail Anderson–Darling methods, and the Nikulin–Rao–Robson test statistic is considered. A simulation study is conducted to assess these methods and to investigate the distribution properties with right-censored data. The applicability of the proposed model is studied based on three real data sets of failure times, bladder cancer patients, and glass fiber data with a comparison with such competitors as the gamma, xgamma, Lomax, Darna, power Darna, power Lindley, and exponentiated power Lindley models. According to several established criteria, the comparative findings are overwhelmingly favorable to the suggested model.

The current paper proposes a new three-parameter probability distribution, called power Darna distribution (PDD), as an extension to the Darna distribution. An extra parameter is added to the base model and aims to increase the flexibility of the model in fitting various real data sets. Different statistical properties as reliability functions, hazard functions, and reversed hazard rate functions are obtained. Additionally, the shapes of the model, moments, inverse moments, and quantile function are derived and discussed. The distribution functions of order statistics from the PDD and moments of the smallest and largest order statistics are presented and a simulation study is conducted for explanation. An estimation of the parameters of PDD based on maximum likelihood estimation is presented. Finally, to demonstrate the PDD applicability in real life situations, a right-censored data set of carcinogenic DMBA in the vaginas of rats is considered and analyzed.

The increasing complexity of modern lifetime data necessitates the development of more flexible probability models. To address this need, we propose the power length-biased new XLindley (PLNXL) distribution, a novel two-parameter model tailored to model a wide range of lifetime datasets. Characterized by both shape and scale parameters, the PLNXL distribution effectively captures diverse hazard rate functions, including increasing, decreasing, and inverted bathtub-shaped forms. Additionally, its mean residual life function is capable of exhibiting decreasing, increasing, and bathtub-shaped behaviors, thereby enhancing its practical relevance. We derive key mathematical properties of the distribution, including moments, reliability measures, and entropy. The parameters are estimated using the maximum likelihood method, and simulation studies confirm the consistency and efficiency of the estimators. The applicability of the proposed model is illustrated using real-world datasets, where it consistently outperforms the existing models. These results highlight the robustness and adaptability of the PLNXL distribution for lifetime data analysis across a wide array of applications.